Problem: Express your answer as a mixed number simplified to lowest terms. $15\dfrac{1}{15}-8\dfrac{3}{6} = {?}$
Solution: Simplify each fraction. $= {15\dfrac{1}{15}} - {8\dfrac{1}{2}}$ Find a common denominator for the fractions: $= {15\dfrac{2}{30}}-{8\dfrac{15}{30}}$ Convert ${15\dfrac{2}{30}}$ to ${14 + \dfrac{30}{30} + \dfrac{2}{30}}$ So the problem becomes: ${14\dfrac{32}{30}}-{8\dfrac{15}{30}}$ Separate the whole numbers from the fractional parts: $= {14} + {\dfrac{32}{30}} - {8} - {\dfrac{15}{30}}$ Bring the whole numbers together and the fractions together: $= {14} - {8} + {\dfrac{32}{30}} - {\dfrac{15}{30}}$ Subtract the whole numbers: $=6 + {\dfrac{32}{30}} - {\dfrac{15}{30}}$ Subtract the fractions: $= 6+\dfrac{17}{30}$ Combine the whole and fractional parts into a mixed number: $= 6\dfrac{17}{30}$